Mat 143 Statistics Empirical Rule and Z Scores

The normal curve is symmetrical about the mean.

• True

• False

At a recent invitational, Emmett ran the 400 in 53.5 seconds with an invite mean of 51 and a SD of 3. Reese ran the 800 in 2 minutes, 1 second with the mean being 2 minutes 46 seconds and SD of 15 seconds.

What were their Z-scores and who performed better?

• Emmett's Z-score was +0.83, Reese's was -3.0. Emmet did better

• Emmett's Z-score was +0.83, Reese's was -3.0. Reese did better because in track lower z-scores are better.

• You can't tell since it's two different events.

• Mr. McDonald can smoke both of 'em.

The average waist size for teenage males is 29 inches with a standard deviation of 2 inches.

If waist sizes are normally distributed, determine the z-score of a teenage male with a 37.5 inch waist.

• 4.25

• 1

• -2

• -1

A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of .25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.

• 2.5%

• 0.15%

• 2.35%

• 2.25%

The mean life of a tire is 30,000 km. The standard deviation is 2000 km.

Then, 68% of all tires will have a life between ___________ km and __________ km.

•  28,000 km and 32,000 km.

• 24,000 km and 34,000 km.

• 26,000 km and 34,000 km.

• 27,000 km and 31,000 km.

A national achievement test is administered annually to 3rd graders. The test has a mean score of 100 and a standard deviation of 15. If Jane's z-score is 1.20, what was her score on the test?

• 82

• 88

• 100

• 118

What percent of people are 3 standard deviations above the mean?

• .15

• 34

• 68

• 2.35

What percent of people are 2 standard deviations or more above the mean?

• 2.35

• 34

• 68

• 2.5

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What is the GPA of the highest 2.5% of the students?

• 4.1 

• 4.1 or higher

• 4.7

• 4.5 or higher

The mean June midday temperature in Desertville is 36°C and the standard deviation is 3°C
Assuming this data is normally distributed, how many days in June would you expect the midday temperature to be between 39°C and 42°C?

• 3

• 4

• 7

• 14